The variable sample size and sampling interval run sum Max chart

ABSTRACT

A variable sample size and sampling interval run sum Max chart (VSSI-RSMax) is proposed to efficiently monitor the mean and/or variability of a process. The VSSI-RSMax chart varies the sample size and sampling interval of the RSMax chart according to the current cumulative score. A Markov chain method is used to evaluate the performance of the proposed chart in terms of the average time to signal (ATS), the adjusted average time to signal (AATS), and the expected AATS (EAATS). The VSSI-RSMax chart is compared with other competitive single control charts, such as the standard fixed sample size and sampling interval (FSSI) Max chart, the VSSI-Max chart, the FSSI-RSMax chart, the FSSI Max-EWMA and the FSSI Max-CUSUM. Also, the implementation of the VSSI-RSMax chart in practice is demonstrated with an illustrative example.

KEYWORDS:

• Adjusted average time to signal
• average sample size
• average sampling interval
• Markov chain
• single control chart
• statistical process control

Acknowledgements

The authors would like to express their gratitude to the three anonymous reviewers for their constructive comments which significantly improved the content and the presentation of this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data used in the example can be found in Tables 6.1 and 6.2 of Montgomery (2013).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/16843703.2024.2315837

Additional information

Notes on contributors

D. L. Antzoulakos

D. L. Antzoulakos, received his Ph.D. in Mathematics from the University of Patras, Greece. He is currently an Associate Professor at the University of Piraeus where he has been teaching since 1997. His research interests include applied probability, statistical process control and distribution theory of runs and patterns.

K. G. Fountoukidis

K. G. Fountoukidis is a PhD candidate at University of Piraeus, Department of Statistic and Insurance Science. He received his Msc in Applied Statistics in 2019 from University of Piraeus and Bsc from University of Aegean, Department of Statistics and Actuarial-Finance Mathematics.

A. C. Rakitzis

A. C. Rakitzis received a PhD in statistics from the University of Piraeus, Greece. He is an Assistant Professor at the Department of Statistics and Insurance Science, University of Piraeus, Greece. He served as an Assistant Professor at the University of the Aegean (Department of Statistics & Actuarial-Financial Mathematics). He has also worked as a postdoctoral researcher (Marie Curie Fellow) at the Universite de Nantes, Institute Universitaire de Technologie de Nantes, France. His research interests include statistical process control and applied probability.